I’m sorry for you, what a huge shock and betrayal. It happened to me also, Ex sent texts to many women. Reflecting back, I still don’t know if my Ex slept with any of them, but it’s highly probable. But honestly it almost doesn’t matter, your husband might not have yet, but you will always know that sleeping together is where it was headed. And honestly the betrayal I think doesn’t have to include sex, it’s big enough.
So I wouldn’t angst too much about whether he has had sex, about who started it. The pain and betrayal is already there for you. He’s already crossed that line and betrayed your trust. It’s a huge emotional betrayal. He’s taken the security right from under you. It’s awful and you need to look after yourself, this can take a toll on not just your emotional health but physically too.
You are now Number One. Just remember that. Everything you do, do for you, your wellbeing, your security, your safety. I’m sorry to say but do go for an STI test no matter what he says. I did and it helped me feel a little more in control and it brings it a little bit more real. You cannot totally believe him at the moment, as he’s lied.
The one good thing is he did immediately tell you once found out. I don’t think this means he hasn’t massively betrayed you. But I do think it shows he has not grown so used to lying and so used to treating you less than human that his immediate response was to cover up and lie again, like most cheaters do.
Good luck. Lots of us have been where you are. It’s horrible. But we do survive.